Various Auto-Correlation Functions of m-Bit Random Numbers Generated from Chaotic Binary Sequences
Abstract
:1. Introduction
2. Auto-Correlation Functions of -Bit Random Sequences
2.1. Definition of Auto-Correlation Function
2.2. Generation of m-Bit Sequences from Binary Sequences
3. Chaotic Binary Sequences with Prescribed Auto-Correlations
4. Numerical Experiments
5. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
References
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(a) | ACF-1 | ACF-1 |
(b) | ACF-2 | ACF-2 |
(c) | ACF-3 | ACF-3 |
(d) | ACF-1 | ACF-4 () |
(e) | ACF-2 | ACF-3 |
(f) | ACF-2 | ACF-4 () |
(g) | ACF-3 | ACF-4 () |
(h) | ACF-4 () | ACF-4 () |
Value | Probability | |||||||
---|---|---|---|---|---|---|---|---|
(-ary Symbol) | (a) | (b) | (c) | (d) | (e) | (f) | (g) | (h) |
0 | 0.125601 | 0.125200 | 0.125324 | 0.124573 | 0.125290 | 0.124844 | 0.124969 | 0.125310 |
1 | 0.125116 | 0.125883 | 0.124778 | 0.125444 | 0.124755 | 0.125496 | 0.125057 | 0.125829 |
2 | 0.124546 | 0.125090 | 0.124958 | 0.125049 | 0.124806 | 0.125352 | 0.125063 | 0.126000 |
3 | 0.125041 | 0.124091 | 0.125284 | 0.125238 | 0.125413 | 0.124572 | 0.125255 | 0.124875 |
4 | 0.124809 | 0.125149 | 0.124792 | 0.124936 | 0.124826 | 0.125353 | 0.124540 | 0.124821 |
5 | 0.124954 | 0.125055 | 0.124779 | 0.124460 | 0.124802 | 0.124458 | 0.124847 | 0.124540 |
6 | 0.125100 | 0.124851 | 0.124749 | 0.124727 | 0.124901 | 0.124467 | 0.124713 | 0.124196 |
7 | 0.124833 | 0.124681 | 0.125336 | 0.125573 | 0.125207 | 0.125458 | 0.125556 | 0.124429 |
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Tsuneda, A. Various Auto-Correlation Functions of m-Bit Random Numbers Generated from Chaotic Binary Sequences. Entropy 2021, 23, 1295. https://doi.org/10.3390/e23101295
Tsuneda A. Various Auto-Correlation Functions of m-Bit Random Numbers Generated from Chaotic Binary Sequences. Entropy. 2021; 23(10):1295. https://doi.org/10.3390/e23101295
Chicago/Turabian StyleTsuneda, Akio. 2021. "Various Auto-Correlation Functions of m-Bit Random Numbers Generated from Chaotic Binary Sequences" Entropy 23, no. 10: 1295. https://doi.org/10.3390/e23101295